CSpace  > 数学所
Xu Xiaoping
Source Publicationsciencechinamathematics
AbstractThe conformal transformations with respect to the metric defining the orthogonal Lie algebra o(n, C) give rise to a one-parameter (c) family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra o(n+2, C). Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector a~→ ∈ C~n, we prove that the space forms an irreducible o(n+2,C)-module for any c ∈ C if a~→ is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of o(n+2,C) on the polynomial algebra C in n variables. Moreover, we prove that C forms an infinite-dimensional irreducible weight o(n + 2, C)-module with finite-dimensional weight subspaces if c 6∈ Z/2.
Document Type期刊论文
Recommended Citation
GB/T 7714
Xu Xiaoping. conformaloscillatorrepresentationsoforthogonalliealgebras[J]. sciencechinamathematics,2016,59(1):37.
APA Xu Xiaoping.(2016).conformaloscillatorrepresentationsoforthogonalliealgebras.sciencechinamathematics,59(1),37.
MLA Xu Xiaoping."conformaloscillatorrepresentationsoforthogonalliealgebras".sciencechinamathematics 59.1(2016):37.
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